Question

Hello, I need some assistance with this homework question please for precalculusHW Q16

Answer 1

SOLUTION:

Case: Shifting a graph

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down. Here are the graphs of y = f (x), y = f (x) + 2, and y = f (x) - 2

Given:

$\begin{gathered} y=x^3 \\ shifting\text{ 8 units up} \end{gathered}$

Required:

To show how the function changes

Method:

Step 1:

The original function

$y=x^3$

At the original function, the graph cuts through (0,0).

Step 2:

When it is shifted 8 units up, the graph will now cut through (0,8).

The function will now be:

$y=x^3+8$

Final answer:

$y=x^3+8$